4 years ago

9.09 repeating as a fraction

Mathematics

1 answer:

rjkz [21]4 years ago

7 0

9.09 as a fraction would be 9 9/100

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Solve the following equation for 0° ≤ θ < 360°. Use the "^" key on the keyboard to indicate an exponent. For example, sin2x w

never [62]

Answer-

$\boxed{\boxed{x=90^{\circ},270^{\circ}}}$

Solution-

The given equation-

$\Rightarrow 2\sin^2 x-\cos^2 x-2=0$

$\sin^2 x+\cos^2 x=1\ \ \Rightarrow \cos^2 x=1-\sin^2 x$

Putting this,

$\Rightarrow 2\sin^2 x-(1-\sin^2 x)-2=0$

$\Rightarrow 2\sin^2 x-1+\sin^2 x-2=0$

$\Rightarrow 3\sin^2 x-3=0$

$\Rightarrow 3\sin^2 x=3$

$\Rightarrow \sin^2 x=1$

$\Rightarrow \sin x=\sqrt1$

$\Rightarrow \sin x=\pm 1$

$\Rightarrow \sin x=1,\ \sin x=-1$

$\Rightarrow x=\sin^{-1}(1),\ x=\sin^{-1}(-1)$

$\Rightarrow x=90^{\circ}+n360^{\circ},\ x=270^{\circ}+n360^{\circ}$

Where n=0, 1, 2, ......

As given 0° ≤ x < 360°, so putting n = 0

$\Rightarrow x=90^{\circ},\ x=270^{\circ}$

3 0

4 years ago

Factor the expression

Alex777 [14]

Factor the equation using difference of squares, which says that a^2-2ab+b^2=(a-b)^2.

a is 2 since the square root of 4 is 2 and b is 5 because the square root of 25 is 5.

Final answer: (2x-5y)^2

8 0

3 years ago

The sum of two numbers is four and their product is ten. If one number is x, write an expression for the other number

lyudmila [28]

Answer:

4y - y^2 = 10

Step-by-step explanation:

Let x and y be the two numbers

x+y = 4

xy = 10

Taking the first equation and solving for x

x = 4-y

Substituting this into the second equation

(4-y) *y = 10

4y - y^2 = 10

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4 years ago

Evaluate the expression when x=-2 y=3 and z = -1/5 xyz=

lakkis [162]

Answer:

Step-by-step explanation:

6 0

3 years ago

One number is 7 less than a second number. Twice the second number is 7 less than 5 times the first. Find the smaller of two num

aliya0001 [1]

N = x-7
2x = 5n-7

2x = 5(x-7)-7
2x=5x-35-7
-3x=-42
x=14
n=7

7 is the answer

8 0

4 years ago